The topological approach to quantum information processing obtains exceptional fault-tolerance by encoding and manipulating information in non-local (i.e., topological) degrees of freedom of topologically ordered systems. Such non-local degrees of freedom typically do not couple to local operations. Consequently, the error rates for topological qubits and computational gates may be exponentially suppressed with distance between anyons and inverse temperature.
This suppression of error rates may provide an advantage over conventional quantum computing platforms. However, it also makes it challenging to coherently transfer quantum information into and out of topological systems. Not only is coupling the non-local degrees of freedom in the topological system to an external system required, but it must be done in a controlled and coherent manner. Consequently, it is desirable to create quantum entanglement between the topological and conventional states.
It is also desirable to create quantum entanglement between conventional states. It would be particularly desirable if there were available apparatus and methods that could be employed for coherently transferring quantum information between conventional-conventional, topological-conventional, and topological-topological qubit pairs.